I am wondering how much of the risk is in the unknown in the first.  

I hope you're buying at a discount to allow for the the unknown repairs.  

How it will apply specifically to your building is unknown. 

I signed a contract at the beginning with a GC that was more general than I wanted considering the large price tag, but he kept saying that he couldn't make it more specific until they busted up the concrete to see what was really going on (lots of unknowns due to age and character of building).

There are many unknowns, its timely, expensive and things don't always go as planned.

The fact that the property makes money hand-over-fist, and the current investor is leaving (for unknown reasons?)

@Stephanie M.If I were a tenant I can't say I'd want some unknown person wandering through my place.

You have two big unknowns right now - one is how much work is needed to be done and how much that will cost, and the other is the use and occupancy permit. 

My questions are: How can I submit a second offer, if it’s unknown that they declined my original offer?

I'm not a fan of investing in small properties located in areas that are not familiar with unknown managers.